Right Triangle Trigonometry Solving Right Triangles Prepared by Title V Staff: Daniel Judge, Instructor Ken Saita, Program Specialist East Los Angeles College EXIT BACKNEXT Click one of the buttons below or press the enter key © 2002 East Los Angeles College. All rights reserved.

Consider a Right Triangle. Note – a is the leg opposite  c is the leg opposite our right angle b is the leg adjacent to  EXIT BACKNEXT

So that we have the following right triangle. EXIT BACKNEXT

The six trigonometric ratios are defined as follows: EXIT BACKNEXT

What are the six trigonometric ratios for  ? Note – We need the length of one of the legs of our right triangle. EXIT BACKNEXT

Use the Pythagorean Theorem... EXIT BACKNEXT

For this triangle we get: hyp adj  opp  EXIT BACKNEXT

Notice we have another angle at . EXIT BACKNEXT

We can obtain the six trigonometric ratios for , HYP opp  adj  hyp EXIT BACKNEXT

Together the model looks as follows. HYP adj  / opp  opp  / adj  hyp With  +  = 90° EXIT BACKNEXT

Recall the 45º - 45º - 90º Special Triangle. What are the six trigonometric ratios for 45º? EXIT BACKNEXT

hyp opp 45º adj 45º EXIT BACKNEXT

hyp opp 45º adj 45º EXIT BACKNEXT

Recall the 30º - 60º - 90º special triangle. What are the six trigonometric ratios for 30 º ? What are the six trigonometric ratios for 60 º ? EXIT BACKNEXT

For 60º hyp opp 60º / adj 30º opp 30º / adj 60º EXIT BACKNEXT

Thus, hyp opp 60º / adj 30º opp 30º / adj 60º EXIT BACKNEXT

For 30º hyp opp 60º / adj 30º opp 30º / adj 60º EXIT BACKNEXT

Thus, hyp opp 60º / adj 30º opp 30º / adj 60º EXIT BACKNEXT

Summary  sin(  )cos(  )tan(  ) 30º 45º1 60º EXIT BACKNEXT

End of Right Triangle Trigonometry Title V East Los Angeles College 1301 Avenida Cesar Chavez Monterey Park, CA Phone: (323) Us At: Our Website: EXIT BACKNEXT